PTTE 434PTTE 434

Economic Analysis of Alternatives

Lecture 9

Part 1Part 1

Discounting and Cashflow Discounting

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The operating premiseThe operating premise ..

The financial value of something today is typically regarded as the future payment stream, however calculated, discounted by some acceptable rate of discount, to a present value.

For example, the value of a bond is equal to the value of all future cash payments (interest and principal redemption) discounted to the future the yield on equivalent bonds.

This discount rate is typically some “opportunity cost” yield.

The slides that follow explain the concept of discounting.

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Some Definitions

Present Value: The amount today that a sum of money in the future is worth, given a specified rate of return.

Future Value: The value of an asset or cash at a specified date in the future that is equivalent in value to a specified sum today.

Cash Flow: The amount of cash a company generates and uses during a period, calculated by adding noncash charges (such as depreciation) to the net income after taxes. Cash Flow can be used as an indication of a company's financial strength. It is also sometimes referred to as the "money value" of trades in a stock during a trading day.

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Some Definitions (Cont’d)

Discounted Cash Flow: A method used to estimate the attractiveness of an investment opportunity.

Cash Flow After Taxes: A company's cash flow after taxes is derived by taking the net income and removing charges for taxes and depreciation.

Life Cycle Cost: The present value sum of all cash flows generated by an investment over the lifetime of that investment (usually after tax). (Note: Government agencies don’t pay taxes, therefore, only the before tax cash flow applies.)

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Some Definitions (Cont’d)

Earnings Before Interest and Tax - EBIT: An indicator of a company's financial performance calculated as revenue minus expenses excluding tax and interest. Also referred to as operating earnings.

Earnings Before Interest After Taxes – EBIAT: An indicator of a company's financial performance calculated as: Revenue - COGS - Expenses (including taxes and excluding interest)

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The Compounding Formula –Calculates “Future Value”

What is the formula for calculating the future value X of the present value X invested at interest rate r (compounded, annual) for n years??

f p

X (1 + r) = Xpn

f

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An example ...

$10 invested for 10 years at 8% compounded annually will be worth:

10 (1.08) = 21.5910

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Present Value Formula

What is the present value X of some guaranteed future value X , assuming the opportunity to invest money today at some compounded interest rate r??

pf

X =X

(1 + r)p

f

n

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The California Lottery

What is the true present value of winning $10 million in the California lottery (paid in 20 equal and annual payments) assuming an interest rate of 8%??

Value =500k

(1.08)i=0

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i = ???

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The California Lottery(continued)

Would would be today's value of the last lottery payment made (in 19 years)??

$500,000 / (1.08) = $115,85619

WHY??

Because $115,856 invested at 8% per year compounded for 19 years would accrue to exactly $500,000.

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A question ...

What is the present value of a promise to pay two payments of $100 each at a date 5 years in the future and again 10 years in the future, if money today can be expected to earn 12% between now and then?

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Present Value Application

X =X

(1 + r)p

f

nUse the present value formula twice and sum the results:

Value5 =$100

(1.12)5 = $56.74

Value10 =$100

(1.12)10 = $32.20

+ = $88.94

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Some basicsDiscounting

P VC F C F C F

1 22

331 0 8 1 0 8 1 0 8( . ) ( . ) ( . )

P VC F

r ii

n

( )11

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Some basics (cont)

Value of a perpetuity cashflow

Constant cashflow:

PVCF

(1+r) 100

08)(1+.$92.59

Cashflow growing at rate g:

PVCF g

1 +(r g)

( ) ( . )

(. .$101.94

1 100 105

08 05)1+

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Why cashflow matters

Modern valuation techniques use discounted present value free cashflow

Cashflow prior to debt use represents the true strength of the company

To survive, a company must have sufficient cashflow to meet amortized debt and similar obligations

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Why cash flow differs from earnings

Some business activities contribute to earnings or constitute expenses, but corresponding cash payments are delayed payables, receivables, inventory.

Some business activities are expensed, but there never is a related cash payment depreciation, amortization, amortization of goodwill.

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Why cashflow differs (cont)

Borrowing and the servicing of debt involve expense and revenue entries that do not correspond to concurrent cash transfers borrowing immediately adds cash but is not

directly expensed loan payments reduce cash, but only the interest

component is expensed

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Debt and Buying Assets

When using debt to buy fixed assets: Borrowing increases cash at the time of the loan Buying the asset decreases cash at the time of the purchase The cost of the loan is expensed only as each payment is

made, and then only interest is expensed as interest expense, principal reduction is not expensed.

The fixed asset is not expensed at time of acquisition, but is depreciated slowly over time.

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Debt financing

Activity Impact uponcash

Impact uponearnings

Borrow the money + None

Buy the equipment - None

Make loan payment - Expense interestonly

Depreciateequipment

None Expensedepreciation

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Depreciation schedules .. 1st five years

Year 3 5 7 10 15 20

1 33.33 20.00 14.29 10.00 5.00 3.75

2 44.45 32.00 24.49 18.00 9.50 7.22

3 14.81 19.20 17.49 14.40 8.55 6.68

4 7.41 11.52 12.49 11.52 7.70 6.18

5 11.52 8.93 9.22 6.93 5.71

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Components of cashflow

Cashflow from operations adjustments for accruals and amortization

Cashflow from financing new debt adds, debt payment substracts

Cashflow for investment (GFA usually) theoretically seen as basis for future value

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Earnings Before Interest and Tax (EBIT) Description

Earnings Before Interest and Tax includes all profits, operating and non-operating, before deducting interest and income taxes.

Earnings Before Interest and Tax (EBIT) is a traditional measurement method that does not include capital costs.

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Earnings Before Interest and Tax (EBIT) Description (Cont’d)

An advantage of EBIT is it is easier to calculate and easier to observe at divisional or sub divisional levels of the firm.

Instead of EBIT also the terms Operating Profit and Operating Earnings are widely used.

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Adjustments to EBIT for cashflow

Accounts Receivable (-)Accounts Payable (+)Inventories (-)Deferred Income Taxes (-)Depreciation (+)

Amortization (+)Amortization of Goodwill (+)

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A Simple Cash Flow Analysis Tool

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Another Example